Calendar: 1899-1900 Page 778

cxxv1 FACULTY OF SCIENCE State the parallelogram of forces and assuming it prove that the moment of any two forces in one plane about any point is equal to the moment of their resultant about the same point Find the position of the centre of gravity of the frustum of solid cone of which the radii of the ends are feet and feet and the height feet Show that any system of forces acting in one plane may be reduced to two forces acting at right angles to one another together with couple twisting about an axis perpen- dicular to the plane Hence find the conditions of equilibrium of such system of forces regular hexagon revolves about one of its sides of length find the surface and also the volume of the ring formed by the revolution FIRST YEAR cj 32 ft per sec per sec body moves from rest under uniform acceleration prove that the distance traversed in any time is proportional to the square of that time body is dropped vertically downwards Find how far it falls in the 3rd sec of its motion and its velocity after it has fallen 100 ft body is projected with velocity of 100 ft per sec at an angle of 45 to the horizon Find the greatest height to which it will rise and its range on horizontal plane through the point of projection mass of 15 lbs rests upon rough horizontal table the coefficient of friction being Ό5 It is connected by string which passes over smooth pulley at the edge of the table to mass of lb hanging freely Find the tension of the string and the distance traversed by the masses in sees Define work and explain how it is measured Shew that the work body of mass can do in virtue of velocity ν is measured by mv2